|
|
A101292
|
|
a(n) = n! + Sum_{i=1..n} i.
|
|
2
|
|
|
1, 2, 5, 12, 34, 135, 741, 5068, 40356, 362925, 3628855, 39916866, 479001678, 6227020891, 87178291305, 1307674368120, 20922789888136, 355687428096153, 6402373705728171, 121645100408832190, 2432902008176640210, 51090942171709440231, 1124000727777607680253
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Called "factoriangular" numbers by Castillo. - N. J. A. Sloane, Aug 30 2016
The only Fibonacci numbers in this sequence are 1, 2, 5, 34. [Ruiz and Luca, verifying a conjecture of Castillo] - Eric M. Schmidt, Nov 07 2017
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n! + n*(n+1)/2.
|
|
EXAMPLE
|
a(3) = 3! + (1 + 2 + 3) = 12.
a(5) = 5! + (1 + 2 + 3 + 4 + 5) = 135.
|
|
MAPLE
|
a:= proc(n) option remember; `if`(n<3, [1, 2, 5][n+1],
((11*n^2+10*n-70)*a(n-1)-(34*n^2-81*n+60)*a(n-2)
+(23*n-10)*(n-2)*a(n-3))/(11*n-24))
end:
|
|
MATHEMATICA
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|